We propose the use of the Kantorovich--Rubinstein norm from optimal transport in imaging problems. In particular, we discuss a variational regularization model endowed with a Kantorovich--Rubinstein discrepancy term and total variation regularization in the context of image denoising and cartoon-texture decomposition. We point out connections of this approach to several other recently proposed methods such as total generalized variation and norms capturing oscillating patterns. We also show that the respective optimization problem can be turned into a convex-concave saddle point problem with simple constraints and hence can be solved by standard tools. Numerical examples exhibit interesting features and favorable performance for denoising and cartoon-texture decomposition.


  1. variational imaging
  2. optimal transport
  3. Kantorovich--Rubinstein distance
  4. total variation
  5. denoising
  6. image decomposition

MSC codes

  1. 49Q20
  2. 94A08
  3. 90B06

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Information & Authors


Published In

cover image SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Pages: 2833 - 2859
ISSN (online): 1936-4954


Submitted: 1 July 2014
Accepted: 2 October 2014
Published online: 18 December 2014


  1. variational imaging
  2. optimal transport
  3. Kantorovich--Rubinstein distance
  4. total variation
  5. denoising
  6. image decomposition

MSC codes

  1. 49Q20
  2. 94A08
  3. 90B06



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